Detecting Mean-Field in Diffusions on a Large Network

Tomoyuki Ichiba, Department of Statistics & Applied Probability, Center for Financial Mathematics and Actuarial Research, and Mathematics, University of California Santa Barbara, USA

We shall consider a detection problem in a large system of stochastic network in continuous time. We describe the system by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. We determine a dichotomy of presence or absence of mean-field interaction, and discuss the problem of detecting its presence from the observation of a single component process. We shall also discuss its discrete-time analogue and corresponding estimation problems.

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